Maximum - practice problems
The maximum is the largest value in a set of numbers or the highest point on a function within a given domain. In calculus, local maxima occur where a function changes from increasing to decreasing, identified by finding where the derivative equals zero and using the second derivative test. Global maxima represent the absolute highest value over the entire domain. Maximum problems are central to optimization, where constraints are used to find the best possible outcome. Applications include maximizing profit, minimizing cost, finding optimal dimensions, and determining extreme values in physics and engineering. Understanding maxima requires knowledge of functions, derivatives, and critical point analysis.Number of problems found: 187
- The perimeter 13
The perimeter of a rectangle is 22 cm. What are its dimensions if it has the maximum possible area? - Four plates
Four equal maximum-sized circular plates are cut from a square sheet of paper with an area of 784 cm². Calculate the circumference of each plate. - Minimum interior angle
What is the minimum interior angle possible for a regular polygon? - Product - maximum
If x+y is 12 then what is the maximum value of x×y? - Soil erosion
From 1842 to 1875, the yearly erosion of 61/100 meters to a maximum of 1 17/50 meters. By how much did these rates of erosion differ? - Latanya
Latanya plans to repaint some classroom bookcases. She has 5 3/5 gallons of paint. All bookcases are the same size, and each requires 1/2 gallon of paint. What is the maximum number of complete bookcases she can paint? - The following 4
The following are the scores of 10 students in a quiz in Teaching Mathematics in the Intermediate Grades subject: 14, 16, 13, 17, 16, 16, 13, 19, 17, and 13. Find the mode and interpret it - Min-max
What is the maximum and minimum of the data set: 6, 2, 3, 3, 2, 2? - A plumber 3
A plumber can buy plastic pipes in 6-foot and 12-foot lengths. The current job requires eight 4-foot lengths, five 5-foot lengths, and three 7-foot lengths. The plumber wants to figure out how many of each of the two stock lengths should be bought to mini - Dogde Caliber
The petrol kilometers M (unit: kilometers per liter) of the Dodge Caliber car is modeled by the function: M(s) = - 1/28 s² + 3 s- 31 What is the car's best petrol kilometers, and what speed is attained? - In a football
In a football tournament of eight teams, where each team played each other exactly once, points were awarded as follows: the winner received 3 points, the loser received 0 points, and in the event of a draw, each team received 1 point. At the end of the t - Cinema visitors
There are 35 seats in each row of an open-air cinema. Determine the maximum number of visitors that can fit in the viewing area, given that the total number of seats is more than 705 and fewer than 740. - Isosceles
A flower bed has the shape of an isosceles triangle with a base of 25 m and legs of 30 m. Calculate the maximum number of flowers that can be planted in this bed, assuming each flower requires approximately 8 dm² of space. Round the result to the nearest - Frames
A framer is to prepare 23 picture frames with dimensions of 30 cm × 42 cm. The strips from which he makes the frames are 3 metres long. a) How many frames can he make from one strip? b) How many strips will he need? - Wrench Lever Force
The key works like a lever, where one arm is the radius of the bolt, and the other is the length of the key. If key no. 12 (for screws with a diameter of 12 mm) and a length of 12 cm can be tightened with a maximum force of 100 N, what force does the wren - Cylindrical bucket
The cylindrical bucket was filled 2/3 with water. You know that the diameter of the bottom is 25 cm, and the water reaches a height of 24 cm. What is the maximum amount of water that can be poured into the bucket? - Pupils 22 Pupils of the graduating class at the Business Academy in Banská Bystrica had from the written test in Slovak language the following marks: 2, 2, 3, 3, 1, 4, 4, 2, 3, 5, 3, 3, 3, 4, 2, 4, 1, 1, 2, 3, 4, 5, 1, 3, 3, 2, 2, 3, 2, 1. Create a frequency distri
- Pool inflow half
The pool has a maximum water capacity of 1200 hl. How many hours will the pool be half complete if the first inflow is 200 l per minute and the second 100 l per minute? - Concorde weight reserve
The maximum take-off weight of the Concorde aircraft is 185,000 kg. What reserve does it have for fuel, passengers, and their luggage if the plane's weight is 78,900 kg? - Tram - safe downhill
What is the maximum angle at which the tram can go downhill to still be able to stop? The coefficient of shear friction is f =0.15.
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